For a system with unit impulse response h[k] = (0.5)k u[k], what is the zero state response y[k] for the input f[k] = (0.8)k u[k] ?
1
\(\rm y[k] = \left[ - \frac{2}{3} (0.5)^k + \frac{7}{3}(0.6)^k \right] u[k]\)
2
\(\rm y[k] = \left[ - \frac{5}{3} (0.5)^k + \frac{8}{3}(0.8)^k \right] u[k]\)
3
\(\rm y[k] = \left[ - \frac{1}{3} (0.5)^k + \frac{2}{3}(0.8)^k \right] u[k]\)
4
\(\rm y[k] = \left[ - (0.5)^k + (0.6)^k \right] u[k]\)